Designing physical structures such as bridges, optical devices and airplanes often boils down to structural optimization, a fundamental family of problems in physical science and engineering [1]}, [2]}, [3]}, [4]}. A primitive version of structural optimization takes the formThis form is also called topology optimization.:
\(\begin{split}\min _{{\mathbf {x}},\mathbf {u}} \mathbf {u}^{{\mathbf {K}}({\mathbf {x}})\mathbf {u} \quad \operatorname{s.t.}{\mathbf {K}}({\mathbf {x}}) \mathbf {u}=\mathbf {f},{\mathbf {V}}({\mathbf {x}}) \le v_0,{\mathbf {x}}\in {0,1}^d,}\end{split}where {\mathbf {x}}\in \mathbb {R}^d is the vectorized binary design variable that indicates where the material should be put to form the structure, \mathbf {u} \in \mathbb {R}^n is the displacement vector, K is the global stiffness matrix, and \mathbf {f} is the vector of external force. For the constraints, {\mathbf {K}}({\mathbf {x}}) \mathbf {u}=\mathbf {f} encodes the physical laws (e.g., Hooke^{\prime }s law) and is often called the \emph {equilibrium constraint}, and {\mathbf {V}}({\mathbf {x}}) = v_0 limits the amount of material to be used.\) 
